Second-harmonic generation from the longitudinal component of vectorial laser beams: a theoretical framework

摘要

Vectorial laser beams propagating beyond the paraxial limit exhibit an intensity profile at focus that depends upon their field structure and the width of their plane wave spectrum. Under tight focussing conditions, the longitudinal component of the lowest order transverse magnetic laser beam has a field amplitude that becomes comparable to that of the transverse components of the beam; the global intensity profile is then narrower than that produced by a Gaussian beam, thus enabling hyperresolution. With a general polarization eigenmode approach for all propagating directions in anisotropic media, we can show that privileged propagating directions exist, allowing preservation of the transverse magnetic polarization state despite birefringence. Using wave functions satisfying the non-paraxial wave equation, we can also find exact expressions for the field components. During propagation of tightly focussed beams along those privileged directions inside an appropriate anisotropic nonlinear crystal, the longitudinal electric field component may then be used to take advantage of nonlinear tensor terms otherwise ineffective with a paraxial beam. In this work, spectral conversion rate and power conversion efficiency of second-harmonic generation are characterized as a function of effective and undepleted nonlinear pumping in the case of propagation along the anisotropic axis of an uniaxial nonlinear crystal. Even if the phase matching condition is not fully satisfied for propagation along this privileged direction, we show to which extent the nonlinear properties are preserved for a restricted interaction volume.